BELL RINGER  Yesterday you learned 3 different ways to solve systems of linear equations. Do you have a preference on how to solve systems? Explain.

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Presentation transcript:

BELL RINGER  Yesterday you learned 3 different ways to solve systems of linear equations. Do you have a preference on how to solve systems? Explain.

SYSTEMS OF LINEAR EQUATIONS CONT. Friday, February 6, 2014

QUICK REVIEW substitution  You can solve systems of linear equations by graphing, substitution, or elimination… but when do you use which one?

WHEN DO YOU GRAPH?  If all equations are in the form y =, then it is easiest to graph (if you have a graphing calculator), but you can always graph if you solve for y first.

WHEN DO YOU SUBSTITUTE?  If only one equation is solved for one variable, then it is usually easiest to use substitution; however, you can always solve one equation for a variable and then substitute.

WHEN DO YOU USE ELIMINATION?  If the systems are already in standard form (Ax + By = C), then it’s easiest to use elimination. Again, you can always change the equations to standard form and then use elimination.

 What are you going to use for your variables?  How do you set up the problem? SYSTEMS IN WORD PROBLEMS

SOLVING BY MATRICES  First, get the system in standard form (Ax + By = C). Then multiply the inverse of the coefficient matrix by the constant matrix to give you the value of the variables. you have to check  If you get an error message “ERR: SINGULAR MAT”, then the equations are either parallel lines or the same line, so there is no solution or infinite solutions (you have to check).

MATRIX EXAMPLES 1. 6x + 2y = a – 9b = -18 3x – 8y = 1 8a – 12b = 24

 Brenda’s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket? SYSTEMS IN WORD PROBLEMS

 A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?

CLASSWORK  Solve the Odd Numbered systems using any of the 4 methods you choose. Feel free to use the same method for each problem, but you are not limited in your choice. SHOW YOUR WORK

HOMEWORK  Solve the Even Numbered systems using any of the 4 methods you choose. Feel free to use the same method for each problem, but you are not limited in your choice. SHOW YOUR WORK